Abstract
For an arbitrary expanding endomorphism of the class \(C^1 \) acting from \(\mathbb {T}^{\infty } \) to \(\mathbb {T}^{\infty } \), where \(\mathbb {T}^{\infty } \) is an infinite-dimensional torus (the quotient space of some Banach space by an integer lattice), we establish the following standard assertions from the hyperbolic theory: the topological conjugacy of this endomorphism with the linear endomorphism of the torus and its structural stability, as well as the presence of the property of topological mixing for this endomorphism if the fundamental set of the torus is bounded.
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Funding
This work was supported by the Russian Foundation for Basic Research, project no. 18-29-10055, and facilitated by the Moscow Center for Fundamental and Applied Mathematics.
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Translated by V. Potapchouck
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Glyzin, S.D., Kolesov, A.Y. & Rozov, N.K. One Class of Structurally Stable Endomorphisms on an Infinite-Dimensional Torus. Diff Equat 56, 1382–1386 (2020). https://doi.org/10.1134/S00122661200100158
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DOI: https://doi.org/10.1134/S00122661200100158